Version 1
: Received: 24 January 2021 / Approved: 26 January 2021 / Online: 26 January 2021 (15:55:06 CET)
Version 2
: Received: 3 February 2021 / Approved: 5 February 2021 / Online: 5 February 2021 (10:13:00 CET)
Kritov, A. Gravitation with Cosmological Term, Expansion of the Universe as Uniform Acceleration in Clifford Coordinates. Symmetry2021, 13, 366.
Kritov, A. Gravitation with Cosmological Term, Expansion of the Universe as Uniform Acceleration in Clifford Coordinates. Symmetry 2021, 13, 366.
Kritov, A. Gravitation with Cosmological Term, Expansion of the Universe as Uniform Acceleration in Clifford Coordinates. Symmetry2021, 13, 366.
Kritov, A. Gravitation with Cosmological Term, Expansion of the Universe as Uniform Acceleration in Clifford Coordinates. Symmetry 2021, 13, 366.
Abstract
The paper briefly reviews the Clifford algebras of space Cl(3,0) and anti-space Cl(0,3) with a particular focus on the paravector representation, emphasizing the fact that both algebras have an isomorphic center represented just by two coordinates. Since the paravector representation allows assigning the scalar element of grade 0 to the time coordinate, we consider the relativity in such two-dimensional spacetime for a uniformly accelerated frame with the constant acceleration 3Hc. Using the Rindler coordinate transformations in two-dimensional spacetime and then applying it to Minkowski coordinates, we obtain the FLRW metric, which in the case of the Clifford algebra of space Cl(3,0) corresponds to the anti-de Sitter (AdS) flat (k=0) case, the negative cosmological term and an oscillating model of the universe. The approach with anti-Euclidean Clifford algebra Cl(0,3) leads to the de Sitter model with the positive cosmological term and the exact form of the scale factor used in modern cosmology.
Keywords
Clifford algebras Cl(3,0) and Cl(0,3); center of Cl(3); two dimensional spacetime of time-volume; constant uniform acceleration; Rindler coordinates; FLRW metric; scale factor; AdS and de Sitter models
Subject
Physical Sciences, Mathematical Physics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received:
5 February 2021
Commenter:
Alexander Kritov
Commenter's Conflict of Interests:
Author
Comment:
The manuscript has been revised based on the reviews received by MDPI experts in the field and according to their requests to make the respective changes.
Commenter: Alexander Kritov
Commenter's Conflict of Interests: Author
according to their requests to make the respective changes.